DIMAT: Decentralized Iterative Merging-And-Training for Deep Learning Models

Recent advances in decentralized deep learning algorithms have demonstrated cutting-edge performance on various tasks with large pre-trained models. However, a pivotal prerequisite for achieving this level of competitiveness is the significant communication and computation overheads when updating these models, which prohibits the applications of them to real-world scenarios. To address this issue, drawing inspiration from advanced model merging techniques without requiring additional training, we introduce the Decentralized Iterative Merging-And-Training (DIMAT) paradigm--a novel decentralized deep learning framework. Within DIMAT, each agent is trained on their local data and periodically merged with their neighboring agents using advanced model merging techniques like activation matching until convergence is achieved. DIMAT provably converges with the best available rate for nonconvex functions with various first-order methods, while yielding tighter error bounds compared to the popular existing approaches. We conduct a comprehensive empirical analysis to validate DIMAT's superiority over baselines across diverse computer vision tasks sourced from multiple datasets. Empirical results validate our theoretical claims by showing that DIMAT attains faster and higher initial gain in accuracy with independent and identically distributed (IID) and non-IID data, incurring lower communication overhead. This DIMAT paradigm presents a new opportunity for the future decentralized learning, enhancing its adaptability to real-world with sparse and light-weight communication and computation.

Neural PDE Solvers for Irregular Domains

Neural network-based approaches for solving partial differential equations (PDEs) have recently received special attention. However, the large majority of neural PDE solvers only apply to rectilinear domains, and do not systematically address the imposition of Dirichlet/Neumann boundary conditions over irregular domain boundaries. In this paper, we present a framework to neurally solve partial differential equations over domains with irregularly shaped (non-rectilinear) geometric boundaries. Our network takes in the shape of the domain as an input (represented using an unstructured point cloud, or any other parametric representation such as Non-Uniform Rational B-Splines) and is able to generalize to novel (unseen) irregular domains; the key technical ingredient to realizing this model is a novel approach for identifying the interior and exterior of the computational grid in a differentiable manner. We also perform a careful error analysis which reveals theoretical insights into several sources of error incurred in the model-building process. Finally, we showcase a wide variety of applications, along with favorable comparisons with ground truth solutions.

Distributed Online Non-convex Optimization with Composite Regret

Regret has been widely adopted as the metric of choice for evaluating the performance of online optimization algorithms for distributed, multi-agent systems. However, data/model variations associated with agents can significantly impact decisions and requires consensus among agents. Moreover, most existing works have focused on developing approaches for (either strongly or non-strongly) convex losses, and very few results have been obtained regarding regret bounds in distributed online optimization for general non-convex losses. To address these two issues, we propose a novel composite regret with a new network regret-based metric to evaluate distributed online optimization algorithms. We concretely define static and dynamic forms of the composite regret. By leveraging the dynamic form of our composite regret, we develop a consensus-based online normalized gradient (CONGD) approach for pseudo-convex losses, and it provably shows a sublinear behavior relating to a regularity term for the path variation of the optimizer. For general non-convex losses, we first shed light on the regret for the setting of distributed online non-convex learning based on recent advances such that no deterministic algorithm can achieve the sublinear regret. We then develop the distributed online non-convex optimization with composite regret (DINOCO) without access to the gradients, depending on an offline optimization oracle. DINOCO is shown to achieve sublinear regret; to our knowledge, this is the first regret bound for general distributed online non-convex learning.

Asynchronous Training Schemes in Distributed Learning with Time Delay

In the context of distributed deep learning, the issue of stale weights or gradients could result in poor algorithmic performance. This issue is usually tackled by delay tolerant algorithms with some mild assumptions on the objective functions and step sizes. In this paper, we propose a different approach to develop a new algorithm, called $\textbf{P}$redicting $\textbf{C}$lipping $\textbf{A}$synchronous $\textbf{S}$tochastic $\textbf{G}$radient $\textbf{D}$escent (aka, PC-ASGD). Specifically, PC-ASGD has two steps - the $\textit{predicting step}$ leverages the gradient prediction using Taylor expansion to reduce the staleness of the outdated weights while the $\textit{clipping step}$ selectively drops the outdated weights to alleviate their negative effects. A tradeoff parameter is introduced to balance the effects between these two steps. Theoretically, we present the convergence rate considering the effects of delay of the proposed algorithm with constant step size when the smooth objective functions are weakly strongly-convex and nonconvex. One practical variant of PC-ASGD is also proposed by adopting a condition to help with the determination of the tradeoff parameter. For empirical validation, we demonstrate the performance of the algorithm with two deep neural network architectures on two benchmark datasets.

MDPGT: Momentum-based Decentralized Policy Gradient Tracking

We propose a novel policy gradient method for multi-agent reinforcement learning, which leverages two different variance-reduction techniques and does not require large batches over iterations. Specifically, we propose a momentum-based decentralized policy gradient tracking (MDPGT) where a new momentum-based variance reduction technique is used to approximate the local policy gradient surrogate with importance sampling, and an intermediate parameter is adopted to track two consecutive policy gradient surrogates. Moreover, MDPGT provably achieves the best available sample complexity of $\mathcal{O}(N^{-1}\epsilon^{-3})$ for converging to an $\epsilon$-stationary point of the global average of $N$ local performance functions (possibly nonconcave). This outperforms the state-of-the-art sample complexity in decentralized model-free reinforcement learning, and when initialized with a single trajectory, the sample complexity matches those obtained by the existing decentralized policy gradient methods. We further validate the theoretical claim for the Gaussian policy function. When the required error tolerance $\epsilon$ is small enough, MDPGT leads to a linear speed up, which has been previously established in decentralized stochastic optimization, but not for reinforcement learning. Lastly, we provide empirical results on a multi-agent reinforcement learning benchmark environment to support our theoretical findings.

Cross-Gradient Aggregation for Decentralized Learning from Non-IID data

Decentralized learning enables a group of collaborative agents to learn models using a distributed dataset without the need for a central parameter server. Recently, decentralized learning algorithms have demonstrated state-of-the-art results on benchmark data sets, comparable with centralized algorithms. However, the key assumption to achieve competitive performance is that the data is independently and identically distributed (IID) among the agents which, in real-life applications, is often not applicable. Inspired by ideas from continual learning, we propose Cross-Gradient Aggregation (CGA), a novel decentralized learning algorithm where (i) each agent aggregates cross-gradient information, i.e., derivatives of its model with respect to its neighbors' datasets, and (ii) updates its model using a projected gradient based on quadratic programming (QP). We theoretically analyze the convergence characteristics of CGA and demonstrate its efficiency on non-IID data distributions sampled from the MNIST and CIFAR-10 datasets. Our empirical comparisons show superior learning performance of CGA over existing state-of-the-art decentralized learning algorithms, as well as maintaining the improved performance under information compression to reduce peer-to-peer communication overhead.

Decentralized Deep Learning using Momentum-Accelerated Consensus

We consider the problem of decentralized deep learning where multiple agents collaborate to learn from a distributed dataset. While there exist several decentralized deep learning approaches, the majority consider a central parameter-server topology for aggregating the model parameters from the agents. However, such a topology may be inapplicable in networked systems such as ad-hoc mobile networks, field robotics, and power network systems where direct communication with the central parameter server may be inefficient. In this context, we propose and analyze a novel decentralized deep learning algorithm where the agents interact over a fixed communication topology (without a central server). Our algorithm is based on the heavy-ball acceleration method used in gradient-based optimization. We propose a novel consensus protocol where each agent shares with its neighbors its model parameters as well as gradient-momentum values during the optimization process. We consider both strongly convex and non-convex objective functions and theoretically analyze our algorithm's performance. We present several empirical comparisons with competing decentralized learning methods to demonstrate the efficacy of our approach under different communication topologies.

Spatiotemporal Attention for Multivariate Time Series Prediction and Interpretation

Multivariate time series modeling and prediction problems are abundant in many machine learning application domains. Accurate interpretation of such prediction outcomes from a machine learning model that explicitly captures temporal correlations can be a major benefit to the domain experts. In this context, temporal attention has been successfully applied to isolate the important time steps for the input time series. However, in multivariate time series problems, spatial interpretation is also critical to understand the contributions of different variables on the model outputs. We propose a novel deep learning architecture, called spatiotemporal attention mechanism (STAM) for simultaneous learning of the most important time steps and variables. STAM is a causal (i.e., only depends on past inputs and does not use future inputs) and scalable (i.e., scales well with an increase in the number of variables) approach that is comparable to the state-of-the-art models in terms of computational tractability. We demonstrate the performance of our models both on a popular public dataset as well as on a domain-specific dataset. When compared with the baseline models, the results show that STAM maintains state-of-the-art prediction accuracy while offering the benefit of accurate spatiotemporal interpretability. We validate the learned attention weights from a domain knowledge perspective for the real-world datasets.

Deep Transfer Learning for Thermal Dynamics Modeling in Smart Buildings

Thermal dynamics modeling has been a critical issue in building heating, ventilation, and air-conditioning (HVAC) systems, which can significantly affect the control and maintenance strategies. Due to the uniqueness of each specific building, traditional thermal dynamics modeling approaches heavily depending on physics knowledge cannot generalize well. This study proposes a deep supervised domain adaptation (DSDA) method for thermal dynamics modeling of building indoor temperature evolution and energy consumption. A long short term memory network based Sequence to Sequence scheme is pre-trained based on a large amount of data collected from a building and then adapted to another building which has a limited amount of data by applying the model fine-tuning. We use four publicly available datasets: SML and AHU for temperature evolution, long-term datasets from two different commercial buildings, termed as Building 1 and Building 2 for energy consumption. We show that the deep supervised domain adaptation is effective to adapt the pre-trained model from one building to another building and has better predictive performance than learning from scratch with only a limited amount of data.

On Higher-order Moments in Adam

In this paper, we investigate the popular deep learning optimization routine, Adam, from the perspective of statistical moments. While Adam is an adaptive lower-order moment based (of the stochastic gradient) method, we propose an extension namely, HAdam, which uses higher order moments of the stochastic gradient. Our analysis and experiments reveal that certain higher-order moments of the stochastic gradient are able to achieve better performance compared to the vanilla Adam algorithm. We also provide some analysis of HAdam related to odd and even moments to explain some intriguing and seemingly non-intuitive empirical results.